An illustration of a scatterplot graph is titled Animal Longevity. It shows x-axis, labeled as average, ranging from 0 to 45 in increments of 5 and y-axis, labeled as maximum, ranging from 0 to 80 in increments of 10.

Question

Multiple points are plotted around a line that points upward to the right with an arrowhead on the top. The line passes approximately through left parenthesis 0 comma 20 right parenthesis, left parenthesis 15 comma 40 right parenthesis, left parenthesis 30 comma 60 right parenthesis, and left parenthesis 40 comma 78 right parenthesis. Two dotted lines are drawn forming a triangle under the line with the line being the hypotenuse. The dotted lines are drawn from left parenthesis 15 comma 40 right parenthesis to left parenthesis 30 comma 40 right parenthesis and from left parenthesis 30 comma 60 right parenthesis to left parenthesis 30 comma 40 right parenthesis. 8 points are plotted close to the line.
Write an equation in slope-intercept form of the trend line.

(1 point)
y=
x +

Answer 1

To find the equation of the trend line in slope-intercept form \(y = mx + b\), we need to determine the slope \(m\) and y-intercept \(b\) of the line.

From the points you have provided:

1. \( (15, 40) \)
2. \( (30, 60) \)

The slope \(m\) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the coordinates of the points: \[ m = \frac{60 - 40}{30 - 15} = \frac{20}{15} = \frac{4}{3} \]

Now that we have the slope \(m = \frac{4}{3}\), we can use one of the points to find the y-intercept \(b\). Let's use the point \( (15, 40) \):

Using the slope-intercept form: \[ y = mx + b \] Substituting \(m\) and the coordinates of the point: \[ 40 = \frac{4}{3}(15) + b \]

Calculating \( \frac{4}{3}(15) \): \[ \frac{4}{3}(15) = 20 \]

So the equation becomes: \[ 40 = 20 + b \]

Solving for \(b\): \[ b = 40 - 20 = 20 \]

Thus, the equation of the trend line in slope-intercept form is: \[ y = \frac{4}{3}x + 20 \]

So, fill in the blanks:

(1 point) y = \(\frac{4}{3}\)x + 20